Abstract: A blow-molding machine having two calibrating stations located on both sides of a centrally arranged extrusion station, and including two closing systems, for one set of blow molds each, is equipped with finishing stations arranged along the longitudinal center plane of the blow-molding machine extending at a right angle to the transverse center plane thereof, for performing pinch-off removal, punching and testing operations, for example. The hollow bodies, which have been blown at the calibrating stations, are fed to the first finishing station in alternating succession by a swinging gripper capable of swinging altogether by 180.degree.. The swinging gripper includes a shell closing system arranged for being pivoted about the swinging axis of the swinging gripper and for being displaced radially relative to that axis. In addition, the shell closing system can be rotated by 180.degree..